SRC/sgebal.f(3)

NAME
SRC/sgebal.f

SYNOPSIS

  Functions/Subroutines
subroutine sgebal (job, n, a, lda, ilo, ihi, scale, info)
SGEBAL

Function/Subroutine Documentation

  subroutine sgebal (character job, integer n, real, dimension( lda, * ) a, integer lda, integer ilo, integer ihi, real, dimension( * ) scale, integer info)

SGEBAL

Purpose:

    !>
    !> SGEBAL balances a general real matrix A.  This involves, first,
    !> permuting A by a similarity transformation to isolate eigenvalues
    !> in the first 1 to ILO-1 and last IHI+1 to N elements on the
    !> diagonal; and second, applying a diagonal similarity transformation
    !> to rows and columns ILO to IHI to make the rows and columns as
    !> close in norm as possible.  Both steps are optional.
    !>
    !> Balancing may reduce the 1-norm of the matrix, and improve the
    !> accuracy of the computed eigenvalues and/or eigenvectors.
    !>

Parameters
    JOB

    !>          JOB is CHARACTER*1
    !>          Specifies the operations to be performed on A:
    !>          = 'N':  none:  simply set ILO = 1, IHI = N, SCALE(I) = 1.0
    !>                  for i = 1,...,N;
    !>          = 'P':  permute only;
    !>          = 'S':  scale only;
    !>          = 'B':  both permute and scale.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the input matrix A.
    !>          On exit,  A is overwritten by the balanced matrix.
    !>          If JOB = 'N', A is not referenced.
    !>          See Further Details.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    ILO

    !>          ILO is INTEGER
    !>

    IHI

    !>          IHI is INTEGER
    !>          ILO and IHI are set to integers such that on exit
    !>          A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
    !>          If JOB = 'N' or 'S', ILO = 1 and IHI = N.
    !>

    SCALE

    !>          SCALE is REAL array, dimension (N)
    !>          Details of the permutations and scaling factors applied to
    !>          A.  If P(j) is the index of the row and column interchanged
    !>          with row and column j and D(j) is the scaling factor
    !>          applied to row and column j, then
    !>          SCALE(j) = P(j)    for j = 1,...,ILO-1
    !>                   = D(j)    for j = ILO,...,IHI
    !>                   = P(j)    for j = IHI+1,...,N.
    !>          The order in which the interchanges are made is N to IHI+1,
    !>          then 1 to ILO-1.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Further Details:

    !>
    !>  The permutations consist of row and column interchanges which put
    !>  the matrix in the form
    !>
    !>             ( T1   X   Y  )
    !>     P A P = (  0   B   Z  )
    !>             (  0   0   T2 )
    !>
    !>  where T1 and T2 are upper triangular matrices whose eigenvalues lie
    !>  along the diagonal.  The column indices ILO and IHI mark the starting
    !>  and ending columns of the submatrix B. Balancing consists of applying
    !>  a diagonal similarity transformation inv(D) * B * D to make the
    !>  1-norms of each row of B and its corresponding column nearly equal.
    !>  The output matrix is
    !>
    !>     ( T1     X*D          Y    )
    !>     (  0  inv(D)*B*D  inv(D)*Z ).
    !>     (  0      0           T2   )
    !>
    !>  Information about the permutations P and the diagonal matrix D is
    !>  returned in the vector SCALE.
    !>
    !>  This subroutine is based on the EISPACK routine BALANC.
    !>
    !>  Modified by Tzu-Yi Chen, Computer Science Division, University of
    !>    California at Berkeley, USA
    !>
    !>  Refactored by Evert Provoost, Department of Computer Science,
    !>    KU Leuven, Belgium
    !>

Definition at line 162 of file sgebal.f.

Author

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